SciTech-Mathmatics-Analysis-Calculus: Difference+Derivative+Integral+Limit:极限(变化测度与量化,高阶)+Series无穷级数

SciTech-Mathmatics-Analysis

Calculus: 微积分

• Difference微分

• Derivative导数

• Integral积分

• Limit:极限(变化的测度与量化,高阶 )

• Series数列/无穷级数

• Field:数域(Closure),

  • Rational Number,
    • 稠密性：任何两个不同Rational Numbers之间，有无穷无尽的Rational Numbers
      例如 c = (a+b)/2;
  • Real Number,
  • Complex Number,
    • \(\large i = \sqrt{-1}\),
    • Euler's Equation: \(\large e^{i\theta} = \cos{\theta} + i \cdot \sin{\theta},\ \theta \in \bm{C}\),

• Number Theory数论:

  • Primes
  • 因式分解
  • Functions

• RealNumberTheory:实数理论

  • 连续Continuity/完备Completeness:
    • Dedkind Split: 不空、不漏、不乱
    • 闭区间套
  • fractions(小数论):
    • Rational fractions:
    • Irrational fractions: 无理数, 无限不循环小数；\(\large \pi,\ e,\ \sqrt{2}\)

• MeasureTheory测度论

• SetTheory集合论(Countable/Uncountable, 可列可加)

  • Set Vs. Element:
    • Set/Collection is collective object, or a "line/
    • Element is considered as individual object. or a "point";
  • Operations:
    • Set-wise operations is cooresponding to and driving by Element-wise operations.